Kinetic, elastic and gravitational potential energy

At the Facility for Rare Isotope Beams (FRIB) isotopes of elements that do not occur naturally can be produced.

FRIB contains a linear accelerator. The initial section of the accelerator is shown.

Explain why the tubes get progressively longer.

A uranium atom (²³⁸₉₂U) has 80 electrons removed. The uranium ion is then accelerated between two adjacent tubes until its kinetic energy is 200 MeV per nucleon.

Calculate the accelerating potential difference.

Show that the uranium ions will reach a velocity of about 65% of the speed of light.

When a uranium ion hits a target at this speed the ion is likely to break up and produce smaller elements. One particular isotope produced in this way is⁴⁰₁₂Mg. The naturally occurring common stable isotope of magnesium is²⁴₁₂Mg. Explain why the break-up of²³⁸₉₂U is likely to produce unusual isotopes such as⁴⁰₁₂Mg.

Over one hundred years ago, Rutherford supervised a series of experiments using a source of alpha particles and thin gold foil.

Describe the model of the atom that Rutherford proposed as a result of this series of experiments.

The initial kinetic energy of an alpha (⁴₂α) particle is 7.310⁻¹³J.

In a textbook, it states that an alpha particle with this energy would be brought to rest when it reached a distance of 5.010⁻¹⁴m from the centre of the

Deduce whether this statement is correct.

Determine the initial momentum of the alpha particle.

An alpha particle moves along a path directly towards a gold nucleus, as shown.

An elastic interaction occurs and the alpha particle recoils.

State what is meant by an elastic interaction.

State what happens to the atoms in the gold foil as a result of these interactions.

Electric vehicles use a direct current (d.c.) electric motor powered by a battery for propulsion. A simplified diagram of a d.c. electric motor is shown.

A split ring consists of two semi‑circular sections that are attached to a coil. The coil is labelled ABCD. Two brushes, made of carbon, rub against and make electrical contact with the split ring.

*(a) Describe how this arrangement can lead to the coil rotating.

An advert for an electric car has the following information:

• electric motor can develop up to 390 kW output power

• car achieves a velocity of 28 m s^–1 from rest in 4.0 s at maximum power

Calculate the work done by resistive forces when the car accelerates to a velocity of

mass of car = 1950 kg

A website suggests that ‘fast‑charging’ the battery in an electric vehicle can increase the internal resistance of the battery.

Explain why an increase in internal resistance of a battery is a disadvantage.

The velocity v of a non‑relativistic particle can be expressed in terms of combinations of the following quantities: kinetic energy E_k, momentum p and mass m. Which of the following expressions is correct?

It was suggested on an online forum that it would be possible to cook a chicken by repeatedly slapping the chicken with one hand.

It was claimed that the energy transferred to a chicken in 8000 slaps would be sufficient to raise the temperature of the chicken from 23 °C to 165 °C.

In an investigation to test the claim, the effective mass of the hand was taken as 1.75 kg and the speed of the hand just before impact with the chicken as 6.25 m s⁻¹.

Deduce whether the data confirms that 8000 slaps would be sufficient. Assume that no energy is transferred from the chicken to the surroundings.

mass of chicken = 0.875 kg specific heat capacity of chicken = 1770 J kg⁻¹K⁻¹ efficiency of energy transfer from the hand = 65%

Explain whether the assumption made in (a) is realistic.

A projectile of mass 65 g is fired vertically upwards into a stationary wooden block of mass 2.400 kg, as shown.

The projectile becomes embedded in the block. They both move vertically upwards through a vertical displacement of 55 cm before momentarily coming to rest.

Calculate the energy dissipated as the projectile hits the block.

Explain how the principle of conservation of energy applies to this collision.

Scientists have been studying a type of jumping spider that can jump up to six times its body length.

The scientists photographed a spider at 0.02s intervals, during a jump. The picture is taken from the photograph and is shown actual size.

Deduce whether the images show that the motion in the x-direction is independent of the motion in the y-direction. You should take measurements using the cross marking the centre of gravity of the spider.

Show that the initial velocity of the spider at the start of the jump is about 1 m s⁻¹. You should take measurements using the cross marking the centre of gravity of the spider.

The spider achieves this jump by extending its two back legs by 3.0 mm.

Calculate the average force the spider exerts in each leg to achieve the jump.

mass of spider = 150 mg

Just as the spider starts the jump, it fixes a silk thread to the platform. It is thought that the thread acts as a safety line in case the spider falls.

A student makes the comment:

ʻIf the silk thread can withstand a tension equal to the weight of the spider then this safety system should work.ʼ

Deduce whether this statement is correct.

At the end of the 19th century, J.J. Thompson used electric and magnetic fields to deflect beams of charged particles. A photograph of his apparatus is shown.

Electrons were accelerated through a potential difference to produce a beam of high-energy electrons. The beam was then deflected in perpendicular directions by the magnetic and electric fields. The final position of the beam on the screen was determined by the charge and mass of the electrons.

Explain how electrons from the source become a beam of high-energy electrons.

An electron is travelling left to right and enters a region of uniform magnetic field as shown below. The direction of the magnetic field is perpendicular to the direction of travel of the electron.

The magnetic field deflects the electron in the direction up the page.

Explain the direction of the magnetic field that would produce this deflection.

Explain why the electron would travel in a circular path if no other forces acted on it.

In a modern version of Thompson’s experiment, a uniform electric field of electric field strength E is applied so that the electric and magnetic forces on the electrons are equal and in opposite directions.

Show that for electrons to be undeflected their velocity must be given by

where B is the magnetic flux density of the magnetic field.

The beam is produced by accelerating electrons through a potential difference of 250 V. The electric field strength is 1.4 × 10⁴V m⁻¹. The magnetic flux density is

Calculate the value of the specific charge e/m for the electron using this data.

In his original experiments, Thompson determined the specific charge of a range of particles. His results indicated that the specific charge of an electron is about 2000 times bigger than that for a hydrogen ion.

Deduce what conclusion can be made from this information.

In the sport of curling, two teams of ‘curlers’ take turns sliding polished granite stones across an ice surface towards a circular target marked on the ice.

A stone of mass 19.6 kg is accelerated uniformly for 1.25 s before being released by a curler. The stone then decelerates uniformly to rest, travelling 32.5 m in a time of 17.5 s.

Calculate the average useful power developed by the curler in accelerating the stone.

*(b) Stone B is stationary. Stone A travels towards the target and makes a direct hit on stone B as shown. Both stones have mass m.

The collision is elastic. Just before the collision stone A has a velocity v. After the collision stone B moves off with velocity v.

Discuss how the relevant conservation laws apply to this collision.

While a stone is moving towards the target, the curlers vigorously sweep the ice directly in front of the stone.

Explain why this may make the stone travel further.

Beam engines contributed to powering the Industrial Revolution in Britain in the 18th century. A beam engine consisted of a beam which could rock to and fro around a well-oiled pivot. Attached to the beam there are two rods, one connected to a piston in a steam cylinder and the other connected to a pump.

The diagram below shows a simplified arrangement of a beam engine.

The beam has a constant thickness and a mass of 3.05 10⁴ kg. The length of the beam is 11.0 m. The pivot P is positioned 6.0 m from the steam cylinder end of the beam.

In its resting position the steam cylinder rod is supported by the base of the steam cylinder with the beam at an angle of 20 to the horizontal.

The steam cylinder rod exerts a force T on the beam. The force exerted on the beam by the pump rod can be neglected.

Calculate the force T.

The engine, which ran continuously, could lift a mass of 2500 kg of water through 12 m each minute. The engine used 1250 kg of coal a day. 1 kg of coal can release 22.3 MJ of energy. The beam engine was said to have an efficiency of 10 %.

Deduce whether this claim for efficiency was correct.

The discovery of the Higgs particle was an important contribution to our understanding of particle physics.

Describe the standard model for subatomic particles. You should identify the fundamental particles and the composition of the particles we can observe.

The mass of the Higgs particle is 2.2 10^–25 kg.

Calculate this mass in GeV/c².

The Higgs particle was discovered using the Large Hadron Collider (LHC) in 2012. Two beams of very high energy protons, moving in opposite directions, were made to collide.

Explain the need for such high energy collisions.

The beams of protons are contained within a ring of superconducting magnets.

Calculate the momentum of a proton in a beam.

magnetic field strength = 8.3 T circumference of the ring = 27 km

State the total momentum of the products of the collision between the two beams of protons.

The LHC accelerates protons until they gain energies of about 7 TeV.

A student used the equation E = to predict the energy of a proton in the beam, using the momentum calculated in (c)(ii), but found the energy was far higher than 7 TeV.

Explain why.

An object of mass m is moved from point A on the ground, to point B on a bench of height h as shown in the diagram.

Which of the following is a correct expression for the work done on the object?

Mass spectrometry is a technique used to separate ions based on their charge to mass ratio.

The atoms in a sample are ionised and then accelerated and formed into a fine beam. This beam is passed into a region of uniform magnetic field and the ions are deflected by different amounts according to their mass.

Analysis of mass spectrometer data shows that chlorine exists in nature as two isotopes, chlorine-35 and chlorine-37.

State what is meant by isotopes.

In a mass spectrometer, chlorine-35 ions are accelerated through a potential difference of 8.50 kV to produce an ion beam.

Show that the speed of singly ionised chlorine-35 atoms is about 2.2 × 10⁵ m s⁻¹.

mass of an ion of chlorine-35 = 34.97 u

In most mass spectrometers the ions are passed through a velocity selector, after being accelerated, to produce a beam of ions of a particular velocity. The velocity selector consists of a pair of parallel plates, across which a potential difference (p.d.) is applied to create an electric field.

In one mass spectrometer the plates are 2.5 cm apart and a p.d. of 135 V is applied.

A magnetic field is also applied to produce a force on the ions in the opposite direction to the force from the electric field. For one particular speed the ions travel in a straight line and emerge from the selector.

Add to the diagram to indicate the directions of the electric field and the magnetic field.

The magnetic flux density applied to the velocity selector is 24.5 mT.

Deduce whether this magnetic flux density is suitable to produce a beam of chlorine-35 ions of speed 2.2 × 10⁵ m s⁻¹.

After passing through the velocity selector the ion beam enters a region of uniform magnetic flux density 0.35 T with the ions travelling at right angles to the field direction.

Explain why the ions travel in a circular path.

Calculate the radius of the circular path.

The diagram shows the path of the chlorine-35 ions in the field. Chlorine-37 ions enter the magnetic field with the same velocity.

1. Add another line to the diagram to show the path of these chlorine-37 ions.

2. Explain any differences in the paths.